Resource Allocation and Decision Analysis (ECON 8010) Spring 2014 Alternative Competitive Environments portions for Exam 1

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1 Resource Allocation and ecision Analysis (ECON 81) Sring 214 Alternative Cometitive Environments ortions for Exam 1 efinitions and Concets: Profit Total Revenues us Total. Primary objective of most rivate enterrise is to maximize rofit Cost-Benefit Princile a rational decision maker should undertake an action if and only if the Marginal Benefit from taking the action is at least as great as the Marginal Cost of doing so. For rofit maximization, think about increasing uantity roduced/sold and comaring Marginal Revenue to Marginal In general, if a firm sells (Q) units of outut each at a rice of (P), then Total Revenue is eual to (Q)(P) => but, the behavior of Marginal Revenue deends greatly uon the Market Structure in which the firm oerates Continuum of Market Structure: Perfect Cometition Intermediate Market Structures (e.g., uooly, Oligooly, Monoolistic Cometition) Monooly Market Power a firm has market ower if: (i) it can increase the rice of its roduct without losing all customers, or euivalently (ii) it must decrease the rice of its roduct in order to sell additional units. Market Power control over rice Firms in erfectly cometitive markets have no market ower [face a horizontal demand curve at the market rice detered by the interlay of market demand and market suly] Firms in imerfectly cometitive markets (i.e., all other market structures) have at least some market ower [ downward sloing demand curve ]

2 Marginal Revenue the change in Total Revenue as uantity sold is increased If demand is given by the Inverse emand Function P (, then R( P (, and it follows that MR( P ( P ( Price Elasticity in terms of Inverse emand: From here, 1 P ( P ( % Q % P Q Q P P => Marginal Revenue can be exressed as 1 P P ( P Q P ( Q MR ( ) P ( ) 1 Fixed costs that do not vary in magnitude as the uantity of outut roduced is changed Variable costs that do vary in magnitude as the uantity of outut roduced is changed 1 Total are eual to the sum of Variable and Fixed : C( VC( F. Average Total Total divided by uantity of outut roduced => C( ATC( Average Variable Variable divided by uantity of outut roduced => VC( AVC( Average Fixed Fixed divided by uantity of outut roduced => F AFC( Average Total are eual to the sum of Average Variable and Average Fixed : C( VC( F VC( F ATC( AVC( AFC( Marginal the change in Total as uantity of outut roduced is increased => MC( C( VC( Efficient Scale the efficient scale of roduction refers to the uantity of outut at which Average Total of roduction are imized. Short Run a eriod of time sufficiently short so that the amount hired/used of at least one inut is eual to some redetered level (based uon a revious decision) In the short run, the fixed inuts are being hired in redetered uantities => fixed costs reresent the redetered costs of hiring these fixed inuts in their redetered uantities

3 Long Run a eriod of time sufficiently long so that the amount hired/used of every inut can be varied In the Long run the firm has the flexibility to hire zero units of every inut => incur zero costs of roduction => fixed costs are eual to zero => all costs are variable Otimal Choice of Outut in Short Run by a firm in a Perfectly Cometitive Market: a firm in a erfectly cometitive market (in which the revailing rice for outut is ) maximizes rofit by: (i) shutting down and roducing units of outut if AVC (ii) roducing the ositive uantity of outut for which MC ( ) (with MC intersecting MR from below ) if AVC

4 Relation between Marginal Revenue and Price for (i) Firm with no market ower faces horizontal demand curve => erfectly elastic demand or MR P ( 1 P ( ( => Marginal Revenue is constant and eual to rice Intuitive: when rice is simly eual to some constant regardless of uantity sold, then selling one more unit always increases revenue by exactly dollars $ P ( => MR( (ii) Firm with some market ower or control over rice Faces downward sloing demand => MR P 1 ( ) ( ) 1 => Thus, for a firm with market ower Marginal Revenue is: Less than Price. Visually: $ ( P Positive 1 (droing rice and increasing uantity demanded leads to greater revenue) Negative 1 (droing rice and increasing uantity demanded leads to less revenue) Eual to zero (which must be true if total revenue is maximized) 1 MR (

5 Grahical illustration of of Production: Minimum level of Average Total $ MC( ATC( AVC( Minimum level of Average Variable Quantity of outut which imizes AVC( Efficient Scale Quantity of outut which imizes ATC( Efficient Scale the efficient scale of roduction refers to the uantity of outut at which Average Total of roduction are imized. For the first unit of outut, Variable are eual to simly marginal costs of the first unit => AVC( must start out eual to MC( But total costs for the first unit consist of more than just variable costs of the first unit => ATC( will start out above MC( Since ATC = AVC + AFC => AFC = ATC AVC AFC is the vertical distance between ATC and AVC Since AFC decreases as ( increases => red curve and blue curve must get closer to each other as ( increases

6 Short Run choice of outut and rofitability of a firm in a Perfectly Cometitive Market: Thus, the short run suly curve of this firm is essentially: the ortion of the Marginal Cost Curve which lies above the Average Variable Cost Curve. Minimum value of AVC $ Short Run Suly Curve of Firm => curve illustrating uantity sulied as a function of rice (at all ossible market rices) MC( AVC( uantity uantity at which AVC are imized For all ossible ositive rices we have that a rofit maximizing firm oerating in a erfectly cometitive market in the short run will: Minimum Value of Average Variable Minimum Value of Average Total Price of Outut Shut own and roduce zero units of outut Earn a rofit of ( F) Produce a ositive uantity of outut Maximum rofit is negative, but greater than ( F) Produce a ositive uantity of outut Able to earn a ositive rofit

7 Multile Choice Questions: 1. is a market structure in which firms sell differentiated roducts (and thus, each firm has some market ower in the Short Run) and in which there are no substantial barriers to entry in the Long Run. A. Monoolistic Cometition B. Oligooly C. Monooly. Perfect Cometition 2. Suose that as the rice of shoes decreases from $4 to $3 Total Consumer Exenditures on shoes increases from $8, to $84,. From this information we can infer that over this rice range demand is A. Inelastic. B. Unit Elastic C. Elastic.. None of the above answers are necessarily correct (based uon the given information).. The Efficient Scale of Production refers to A. the level of outut above which all Fixed can be avoided. B. the level of outut which imizes Average Fixed of roduction. C. the level of outut which imizes Average Total of Production.. the level of outut at which Marginal of Production become negative. 8. For a firm with market ower, while for a firm in a erfectly cometitive market. A. Marginal Revenue is eual to Price; Marginal Revenue is less than Price. B. Marginal Revenue is less than Price; Marginal Revenue is greater than Price. C. Marginal Revenue is less than Price; Marginal Revenue is eual to Price.. Marginal Revenue is greater than Price; Marginal Revenue is eual to Price. 9. The is defined as a eriod of time sufficiently long so that the amount hired/used of every factor of roduction can be altered. A. Profitability Stage B. Efficient Scale of Production C. Short Run. Long Run 12. The states that a rational decision maker should undertake an action if and only if the Marginal Benefit from taking the action is at least as great as the Marginal Cost of doing so. A. Cost-Benefit Princile B. Incentive Princile C. Inverse Elasticity Pricing Rule. Herfindahl-Hirschman Index 13. In which of the following industry structures should a firm exect to earn zero rofit in the Long Run? A. Perfect Cometition. B. Monoolistic Cometition. C. Monooly.. More than one (erhas all) of the above answers is correct.

8 For uestions 14 through 17, consider a firm with costs of roduction as illustrated below: $ ATC ATC( AVC( AVC.6 uantity 2 8 1, 14. Based uon the grah above, this firm is currently oerating in the A. Long Run, since no Marginal Cost Curve has been drawn. B. Long Run, since Average Fixed clearly increase as more outut is roduced. C. Short Run, since Marginal of roduction are clearly ositive.. Short Run, since Fixed of Production are clearly ositive. 1. The Marginal Cost of roducing the 9 th unit of outut must be A. exactly eual to $.6. B. greater than $.6, but less than $7.2. C. exactly eual to $7.2.. greater than $ The Efficient Scale of roduction is eual to units of outut. A. B. 2 C. 8. 1, 17. If this firm were to roduce 1, units of outut, Average Variable of Production would be eual to A.. B. $.6. C. $.7.. $8.7.

9 22. Scott sells turnis in a small, rural town in Oklahoma. Since he is the only turni seller in town, he has some market ower. He is currently charging $1.7 for each five ound bag of turnis, a rice at which he sells 4 bags er month. If he were to increase his uantity sold to bags er month A. he would have to decrease the rice he charges. B. his Average Total of roduction would have to be lower. C. his Total Revenue would have to increase.. More than one (erhas all) of the above answers is correct. For uestions 23 through 2, consider a firm in a erfectly cometitive market with costs of roduction as illustrated below: 12. $ MC( ATC( 9. ATC 8. AVC( 6.. AVC 4.3 MC 3.1 uantity 8 1,4 2, 2,4 23. If this firm were to roduce zero units of outut in the short run, then A. it would earn zero rofit. B. it would earn a rofit of $( 2,2). C. it would earn a rofit of $( 6,).. it would earn a rofit of $( 6,9). 24. If the er unit rice of outut in this market were $12., then this firm would A. roduce 2,4 units of outut. B. incur Variable of Production eual to $1,6. C. earn a rofit of $13,2.. More than one (erhas all) of the above answers is correct. 2. This firm will roduce a ositive uantity of outut in the short run but earn a negative rofit if and only if the er unit rice of outut is A. less than $3.1. B. less than $4.3. C. exactly eual to $4.3.. greater than $4.3 but less than $8..

10 26. Average Total of Production A. are eual to Average Variable of Production lus Average Fixed of Production. B. are defined as Fixed of Production divided by uantity of outut roduced. C. can never be less than Average Variable of Production.. More than one (erhas all) of the above answers are correct. 27. The short run suly curve of a firm in a erfectly cometitive market is A. a horizontal line at the revailing market rice. B. a horizontal line at the imum value of Average Total of Production. C. the ortion of the Marginal Cost curve which lies above the Average Variable Cost Curve.. the ortion of the Marginal Cost curve which lies above the Average Total Cost Curve. 29. Consider a firm in a erfectly cometitive market with: outut rice of $4.9 er unit; AVC $.2; and ATC $6.8. When maximizing rofit in the short run, this firm A. will shut-down and earn a negative rofit. B. will shut-down and earn zero rofit. C. will roduce a ositive uantity and earn a negative rofit.. will roduce a ositive uantity and earn a ositive rofit. 3. refer(s) to inut costs that do not reuire an outlay of money by the firm. A. Profit B. Imlicit C. Exlicit. Accounting 31. If a firm made an Accounting Profit of $7, last year, then the Economic Profit of the firm A. must have been greater than $7,. B. must have also been eual to $7,. C. must have been less than $7, (but had to have been ositive).. must have been less than $7, (and could have been either ositive or negative).

11 Problem Solving or Short Answer Questions: 1. Consider a market in which demand is given by the demand function ( ) 16, 2,. 1A. Is demand Elastic, Inelastic, or Unit Elastic at a rice of 2? Exlain. 1B. If rice were to decrease from to. 89 would Total Consumer Exenditures on this good increase, decrease, or remain constant? Exlain. 1C. Is it ossible for Total Consumer Exenditures on this good to eual $3,? Clearly exlain why or why not. 2. Consider a firm oerating in a erfectly cometitive market with roduction costs of 2 C ( 1 8 2,. 2A. etere exressions for MC (, AVC (, and ATC ( for this firm. 2B. etere an exact rice above which the firm will choose to sell a ositive uantity of outut in the Short Run and below which the firm will choose to shutdown in the Short Run. 2C. etere a function which secifies the uantity of outut that this firm will choose to roduce in the Short Run (as a function of market rice, ). 2. For what range of values of is this firm able to earn a ositive rofit in the Short Run? For what range of values of is this firm not able to earn a ositive rofit in the Short Run? Exlain. 3. Consider a firm oerating in a erfectly cometitive market with roduction costs of C ( ,. 3A. etere the functional form of MC (. 3B. etere the functional form of AVC (. 3C. etere the functional form of ATC (. 3. etere an exact rice above which the firm will choose to sell a ositive uantity of outut in the Short Run and below which the firm will choose to shutdown in the Short Run. 4. Consider a firm with roduction costs of, facing demand of. 4A. etere the er unit rice that this firm would set and the uantity of outut that this firm would sell in order to maximize rofit. 4B. For what range of values of is this firm able to earn a ositive rofit in the Short Run? For what range of values of is this firm not able to earn a ositive rofit in the Short Run? Exlain.

12 . Consider a firm oerating in a erfectly cometitive market in the Short Run. The table below rovides a artial summary of costs of roduction for this firm. (Assume throughout that the firm is restricted to choosing from only the uantities of outut corresonding to each of the rows in the table below; in this context, Marginal are eual to the change in Total divided by the change in Quantity of Outut roduced that is, MC TC Q ). Quantity of Outut Variable Fixed Total Marginal Average Variable Average Fixed Average Total 2, 2, 2 179,2 6, 6,64 4 2, 4, ,6 2,4,4 2, 4,67 A. Comlete the table above by correctly filling in all of the missing numerical values. B. If this firm is able to sell its outut for $3, er unit, how much outut would it sell, how much revenue would it earn, and is it able to earn a ositive rofit? C. If this firm is able to sell its outut for $, er unit, how much outut would it sell, how much revenue would it earn, and is it able to earn a ositive rofit? 6. an is the President and CEO of Owl Softdrinks, the roducer of Scray Cola. The consumer research division of Owl Softdrinks recently told an that under current market conditions (i.e., for the demand that the firm currently faces and at the rice that the firm is currently charging) the Price Elasticity of emand for Scray Cola is aroximately (.79). Assug that this value has been estimated correctly, what can you infer about the current ricing and outut decision of this firm? 7. Consider a firm with roduction costs of, facing demand given by the inverse function. 7A. etere exressions for and for this firm. 7B. etere the er unit rice that this firm would set and the uantity of outut that this firm would sell in order to maximize rofit. 7C. etere the uantity of outut that would maximize Total Social Surlus in this market. 7. etere numerical values for Total Consumers Surlus, Total Producer s Surlus, Profit, and eadweight-loss in this market. 7E. etere an exression for Price Elasticity of emand as a function of uantity sold for the inverse demand function given above. 7F. Verify that when maximizing rofit, the firm is choosing a rice and uantity for which the Inverse Elasticity Pricing Rule is satisfied.

13 Answers to Multile Choice Questions: 1. A 2. C 3. A 4. B. C C 8. C C A B C B 2. B 21. B 22. A 23. C C 28. C 29. A 3. B 31. Answers to Problem Solving or Short Answer Questions: 1A. Inelastic. Note that the given demand function of ( ) 16, 2, describes a linear demand relationshi. The corresonding linear demand curve has a vertical intercet of 8 and a horizontal intercet of 16,. Thus, the oint along the demand curve at a rice of 2 lies on the bottom half of the demand curve. Recall that for any linear demand curve, demand is Inelastic along the bottom half of the curve. 1B. Increase. A decrease in rice from to. 89 is a movement down this linear demand curve along the to half of the demand curve. Recall that for any linear demand curve, demand is Elastic along the to half of the curve. Further, when

14 demand is Elastic, a decrease in rice will (in general) lead to an increase in Total Consumer Exenditures on the good. Thus, this decrease in rice leads to an increase in Total Consumer Exenditures. 1C. No, given this demand function it is not ossible for Total Consumer Exenditures to eual $3,. Recall that in general Total Consumer Exenditures can be increased: if demand is Elastic by decreasing rice, and if demand is inelastic by increasing rice. It follows that along any linear demand curve, Total Consumer Exenditures are maximized at the one oint where demand is unit elastic (the halfway oint of the curve ). For the demand function ( ) 16, 2, this halfway oint corresonds to a rice of 4 and uantity of 8,. Thus, Total Consumer Exenditures are maximized when 8, units are urchased each at a rice of $4. This leads to Total Consumer Exenditures of ( )( ($4)(8,) $32, $3,. 2A. Given the cost function ( ) C, : MC C( 2, 8 ( 4 VC( 1 C( 1, AVC ( 8 2, and ATC( B. The firm will choose to sell a ositive uantity of outut in the Short Run if and only if rice is greater than the imum value of Average Variable of roduction. From VC( 1 the function AVC ( 8 2, it is straightforward to see that the imum value of Average Variable over all ossible is realized at : AVC AVC() 2. 2C. So long as rice is greater than or eual to $2, the firm maximizes rofit by roducing the ositive uantity for which MC(. Given MC 1 2, this condition is ( Solving for as a function of, we obtain S ( ) 4 8,. 2. A firm in a erfectly cometitive market will be able to earn a ositive rofit in the Short Run so long as rice is greater than the imum value of Average Total of roduction. Recall that at the oint where ATC ( achieves its imum value, we must have MC( ATC(. Thus, we can detere the uantity of outut that imizes ATC ( by setting MC( ATC( and solving for. oing this:, 1 ATC( MC( ) 2 4,, 2,. From here it follows that ATC ATC (2,) 2. Therefore, the firm is able to earn a ositive rofit in the Short Run if and only if er unit rice is above $2. 3A. For ( ) C 22 1, we have MC ( C( B. For ( ) VC( 2 1 C 22 1, we have AVC ( C. For ( ) C( 1 2 1, C 22 1, we have ATC( 22.

15 3. In the Short Run the firm maximizes rofit by shutting-down and selling zero units of outut if and only if rice is below the imum value of Average Variable of Production. Recall that at the oint where AVC ( achieves its imum value, we must have MC( AVC(. Thus, we can detere the uantity of outut that imizes AVC ( by setting MC( AVC( and solving for. oing this: ) ( AVC MC ) 22.. ( From here it follows that AVC AVC Therefore, the firm will choose to sell a ositive uantity of outut in the Short Run if and only if er unit rice is above $2.7. A. (cells with values initially given are highlighted in yellow) Quantity of Outut Variable Fixed Total 139,2 139,2 Marginal Average Variable Average Fixed Average Total 1 2, 139,2 19,2 2, 2, 13,92 1,92 2 4, 139,2 179,2 2, 2, 6,96 8,96 3 6, 139,2 199,2 2, 2, 4,64 6,64 4 8, 139,2 219,2 2, 2, 3,48,48 12, 139,2 241,2 2,2 2,4 2,784 4, ,6 139,2 266,8 3,2 2,2 2,4 4, , 139,2 299,2,4 2, 2,17 4,67 B. If the firm is able to sell its outut at a rice of $3, er unit, then its Marginal Revenue is eual to $3, for each unit sold. From the values reorted for Marginal in the table above, it follows that the otimal uantity to sell in this case would be units. This would give the firm Total Revenue of $1,. But, since the firm would be incurring Total of $241,2, the rofit of the firm is eual to $( 91,2). C. If the firm is able to sell its outut at a rice of $, er unit, then its Marginal Revenue is eual to $, for each unit sold. From the values reorted for Marginal in the table above, it follows that the otimal uantity to sell in this case would be 8 units. This would give the firm Total Revenue of $29,. Since the firm would be incurring Total of $266,8, the rofit of the firm is eual to $(23,2).